Reduced four-wave mixing and Raman amplification architecture

ABSTRACT

Raman amplifiers with improved signal to noise ratio and four-wave mixing product suppression are provided. In one embodiment, both co-propagating and counter-propagating pump energy are employed to cause Raman amplification effects within a fiber. Improved Raman amplification performance including improved four-wave mixing product suppression facilitates longer distance transmission without regeneration of optical signals and/or denser WDM channel spacings.

STATEMENT OF RELATED APPLICATIONS

The present application claims priority from U.S. Provisional App. No.60/279,854, entitled INTERACTION OF FOUR-WAVE MIXING AND DISTRIBUTEDRAMAN ARCHITECTURE and filed on Mar.28, 2001 and is a continuation ofU.S. patent application Ser. No. 09/899,872, filed Jul. 5, 2001, nowU.S. Pat. No. 6,867,905, all of which are incorporated herein byreference for all purposes in their entirety.

BACKGROUND OF THE INVENTION

The present invention relates to optical communication systems and moreparticularly to amplification in optical communication systems.

The explosion of communication services, ranging from videoteleconferencing to electronic commerce, has spawned a new era ofpersonal and business interactions. As evident in the rapid growth ofInternet traffic, consumers and businesses have embraced broadbandservices, viewing them as a necessity. However, this enormous growth intraffic challenges the telecommunication industry to develop technologythat will greatly expand the bandwidth of existing communicationsystems. Further improvements in optical communications hold greatpromise to meet continuing demands for greater and greater bandwidth.

Wavelength Division Multiplexing (WDM) technology, in particular DenseWDM (DWDM) techniques, permits the concurrent transmission of multiplechannels over a common optical fiber. The advent of Erbium Doped FiberAmplifiers (EDFAs) has accelerated the development of WDM systems byproviding a cost-effective optical amplifier that is transparent to datarate and format. An EDFA amplifies all the wavelengths simultaneously,enabling the composite optical signals to travel large distances (e.g.,600 km or greater) without regeneration.

One of the principal limitations of EDFA technology is limitedbandwidth. Discrete and distributed Raman amplifiers have been developedto overcome this limitation. They provide very high gain across a widerange of wavelengths. Moreover, discrete and distributed Ramanamplifiers increase the distance between optical regeneration points,while allowing closer channel spacing. The operation of Raman amplifiersinvolves transmitting high-power laser pump energy down a fiber. Thepump energy amplifies the WDM signal.

The performance of Raman amplifiers in DWDM systems is limited byvarious impairments. One such impairment is four-wave mixing, a commondetriment to optical communication system performance. If threewavelength components of a DWDM signal located at the opticalfrequencies f₁, f₂, and f₃ are being amplified, non-linear effects willcause generation of an undesired fourth component at f_(fwm)=f₁+f₂−f₃.This undesired fourth component is a four-wave mixing product. Thefour-wave mixing product represents a noise-like impairment that canaffect reception of a WDM channel at or near f_(fwm).

Suppressing the generation of four-wave mixing products has been a keyconcern in the design of Raman amplifiers, both discrete anddistributed. In particular, the desire to limit four-wave mixing effectshas led Raman amplifier designers to inject pump energy into a fiberexclusively in a counter-propagating direction relative to thepropagation direction of the signal to be amplified. Unfortunately, suchan approach also concentrates the amplification effects towards the endof the fiber, limiting the signal to noise ratio performance of theRaman amplifier.

What is needed are systems and methods for improving both four-wavemixing product suppression and signal to noise ratio in Ramanamplifiers.

SUMMARY OF THE INVENTION

Raman amplifiers with improved signal to noise ratio and four-wavemixing product suppression are provided by virtue of one embodiment ofthe present invention. In one embodiment, both co-propagating andcounter-propagating pump energy are employed to cause Ramanamplification effects within a fiber. The resulting improved performanceincluding improved four-wave mixing product suppression facilitatesdenser WDM channel spacings and/or longer distance transmission withoutregeneration of optical signals.

According to a first aspect of the present invention, apparatus foramplifying an optical signal includes: a fiber and an optical pumpenergy source disposed to inject optical pump energy into the fiber in aco-propagating direction relative to a transmission direction of anoptical signal in the fiber to cause Raman amplification of the signalin accordance with a gain level. The gain level is greater than 4 dB.

According to a second aspect of the present invention, apparatus foramplifying an optical signal includes: a first optical pump energysource disposed to inject optical pump energy into a fiber in aco-propagating direction relative to a transmission direction of theoptical signal to cause Raman amplification of the signal in accordancewith a first gain level, and a second optical pump energy sourcedisposed to inject optical pump energy into the fiber in acounter-propagating direction relative to the transmission direction ofthe optical signal to cause Raman amplification of the signal inaccordance with a second gain level. The optical signal experiences atotal gain level includes the first gain level and the second gainlevel. The first gain level is greater than 4 dB.

Further understanding of the nature and advantages of the inventionsherein may be realized by reference to the remaining portions of thespecification and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an optical amplification architecture according to oneembodiment of the present invention.

FIG. 2 depicts a first contour showing the tradeoff between per channelinput power and forward Raman gain for a constant optical signal tonoise ratio and a second contour showing the tradeoff between four wavemixing-induced crosstalk and forward Raman gain for a constant forwardgain saturation according to one embodiment of the present invention.

FIG. 3 is a graph depicting the relationship between cross-gainmodulation and gain saturation according to one embodiment of thepresent invention.

FIG. 4 is a graph depicting the relationship between double Rayleighback-scattering and Raman gain according to one embodiment of thepresent invention.

DESCRIPTION OF SPECIFIC EMBODIMENTS

One embodiment of the present invention is directed toward a Ramanamplifier configuration that employs both co-propagating andcounter-propagating optical pumps. The inventors have discovered thatsuch a configuration may achieve a better combination of four-wavemixing product suppression and amplifier output signal to noise ratiothan could be achieved with prior art systems employing acounter-propagating optical pump signal alone. Previously, designershave either failed to take advantage of co-propagating pump energy orused insufficient co-propagating pump energy to realize the advantagesattainable by embodiments of the present invention.

More particularly, a Raman amplifier according to the present inventionemploying both counter-propagating and co-propagating optical pumps mayachieve greater four-wave mixing product suppression than a Ramanamplifier using only a counter-propagating pump to achieve the same gainand output signal to noise ratio. Alternatively, a Raman amplifieraccording to the present invention may achieve a higher output signal tonoise ratio than a Raman amplifier using only a counter-propagating pumpto achieve the same gain and four-wave mixing product suppression.

FIG. 1 depicts an optical amplification architecture according to oneembodiment of the present invention. An optical link 100 connects a WDMtransmitter and a WDM receiver. Of the WDM transmitter, only amultiplexer 102 and an output erbium-doped fiber amplifier (EDFA) 104having gain G_(A) are depicted. Of the WDM receiver, only ademultiplexer 106 and a receiver block 108 for a single WDM channel aredepicted. Further details of the WDM transmitter and WDM receiver arenot germane to the present invention. Also, chromatic dispersioncompensation components are omitted for ease of description andillustration.

In this example, there is no regeneration of the optical signal alongthe link. All amplification is purely optical. For the purpose ofamplification, the link is divided into 25 spans. For ease ofillustration, only a single span 110 is depicted. Typically, each of thespans incorporates similar components. In a particular example, eachspan represents 125 km of TW-RS™ fiber available from LucentTechnologies. Link 100 thus extends for 3125 km. Link 100 carries 32 WDMchannels spaced 50 GHz apart and centered at approximately 1545 nm. Thedispersion of the fiber at this wavelength is D=4.18 ps/nm/km.

The fiber of each span introduces approximately 25 dB of loss. Tocompensate for this loss, each span incorporates an EDFA 112 havingG_(A). In one embodiment, G_(A)=10 dB and EDFA 112 has a 7 dB noisefigure. To provide the remaining needed compensation for span loss, (15dB here) a Raman amplifier 113 is also included. Raman amplification isinduced in a fiber 115 by use of both a co-propagating pump 114 and acounter-propagating pump 116. Pumps 114 and 116 are coupled into fiber115 by couplers 118 and 120 respectively. The operation ofco-propagating pump 114 gives rise to a forward Raman gain, G_(F), whilethe operation of counter-propagating pump 116 gives rise to a backwardRaman gain, G_(B). The pumps emit energy at 1445 nm

Methods and criteria for selecting G_(F) and G_(B) for optimal linkoperation will now be described. Performance criteria to be consideredinclude signal to noise ratio, four-wave mixing product suppression,double Rayleigh backscattering product suppression, cross-gainmodulation due to amplifier saturation, etc.

FIG. 2 is a graph depicting the relationship between four-wavemixing-induced cross-talk and forward Raman gain according to oneembodiment of the present invention. The following is the theoreticalbasis for the data determined in FIG. 2.

The four-wave mixing cross product can be expressed as:

$\begin{matrix}{{X_{F}(L)} = {\frac{P_{F}}{P_{ch}} = {\left( {\gamma\frac{D_{pqr}}{3}} \right)^{2}P_{ch}^{2}{{\int_{0}^{L}{{G(\zeta)}{\mathbb{e}}^{{\mathbb{i}}\;{\Delta\beta}\;\zeta}\ {\mathbb{d}\zeta}}}}^{2}}}} & (1)\end{matrix}$

The term L refers to fiber length.

The term P_(F) refers to the four-wave mixing product power.

The term P_(ch) refers to power per channel at the fiber input.

The term γ refers to a non-linear coefficient of the fiber,

$\gamma = \frac{2\pi\;\eta_{2}}{\lambda\; A_{e}}$where η₂ is the refraction index of the fiber and A_(e) is the effectivearea of the fiber as explained in R. W. Tkach, and A. R. Chraplyvy,“Fiber Nonlinearities and Their Impact on Transmission Systems” in I. P.Kaminov and Thomas L. Koch, “Optical Fiber Communication IIIA,” AcademicPress 1997, (hereinafter “Forghieri”) the contents of which are hereinincorporated by reference.

The term D_(pqr) is equal to 6 for three-tone products as explained inForghieri.

The term G(ξ) refers to the gain as it has evolved at a distance ξ alongthe fiber.

The term Δβ refers to the phase mismatch parameter and is defined by:

$\begin{matrix}\begin{matrix}{{\Delta\beta} = {\beta_{p} + \beta_{q} - \beta_{r} - \beta_{F}}} \\{= {\frac{2\pi\;\lambda^{2}}{c}\left( {f_{p} - f_{r}} \right){\left( {f_{q} - f_{r}} \right)\left\lbrack {{D(\lambda)} - {\frac{\lambda^{2}}{c}\left( {\frac{f_{p} + f_{q}}{2} - f} \right)\frac{\mathbb{d}D}{\mathbb{d}\lambda}}} \right\rbrack}}}\end{matrix} & (2)\end{matrix}$as presented in Forghieri.

The term λ refers to a generic wavelength. The term ƒ refers to thefrequency corresponding to this generic wavelength.

The terms ƒ_(p), ƒ_(q), ƒ_(r) refer to the frequencies of the channelsgiving rise to the mixing products.

The term D(λ) refers to chromatic dispersion at wavelength λ.

The integral in 1) can be approximated as:

$\begin{matrix}{{\int_{0}^{L}{{G(z)}{\exp\left( {{\mathbb{i}}\;{\Delta\beta}\; z} \right)}\ {\mathbb{d}z}}} \approx \frac{1 + {G_{F}G_{B}{\exp\left( {{- \alpha_{\Lambda}}L} \right)}}}{{\mathbb{i}}\;{\Delta\beta}}} & (3)\end{matrix}$

The term α, refers to the fiber attenuation at the pump wavelength.

$\begin{matrix}{P_{{ASE},K} = {2h\;{\upsilon\Delta\upsilon}{\int_{0}^{L}{r_{0}{N_{p}(\xi)}{\exp\left( {{- {\alpha_{s}\left( {L - \xi} \right)}} + {\int_{\xi}^{L}{r_{0}{N_{p}(\eta)}\ {\mathbb{d}\eta}}}} \right)}\ {{\mathbb{d}\xi}.}}}}} & (4)\end{matrix}$

The term hυ refers to the photon energy.

The term Δυ refers to the bandwidth over which the noise power ismeasured.

The term r₀ refers to the Raman gain coefficient of the fiber.

The pump photon number N_(p)(z) is proportional to the pump power and,in the unsaturated gain approximation, is described by the formula:

$\begin{matrix}{{N_{p}(z)} = {\frac{1}{r_{0}}\frac{1}{L_{{eff},p}}\left( {{{\ln\left( G_{F} \right)}{\mathbb{e}}^{{- \alpha_{p}}z}} + {{\ln\left( G_{B} \right)}{\mathbb{e}}^{\alpha_{F}{({1,z})}}}} \right)}} & (5)\end{matrix}$

The term α_(p) refers to the fiber attenuation at the pump wavelength.

The term L_(eff, p) refers to the effective fiber length at the pumpwavelength and is given by:L _(eff,p)=(1−exp(−α_(p) L))/α_(p)  (6)

P_(ASE.EDFA) is the ASE generated within the EDFA and is given by:P _(ASE.EDFA)=2hυΔυ(G _(A)−1)n _(sp).  (7)

The term n_(sp) refer to population inversion factor.

FIG. 2 is a useful tool in selecting values for G_(F) and G_(B). The xaxis of the graph of FIG. 2 represents unsaturated forward Raman gain.The left y-scale of the graph of FIG. 2 represents input power perchannel to fiber 115. The right y-scale of FIG. 2 reports thecorresponding four-wave mixing-induced cross talk at the end of thewhole link of 25 spans assuming that G_(B) provides the remainder of the15 dB that G_(F) does not provide. To get this crosstalk, individualcontributions from each span are added.

FIG. 2 assumes a dispersion value of D=4.185 ps/nm/km at the relevantwavelengths and an effective area, A_(eff)=55 μm². The data points ofFIG. 2 and the relationship between channel power and four-wave mixingproduct suppression assume that within the 15 dB gain budgeted for Ramanamplifier 113, gain not provided by the operation of the co-propagatingpump (G_(F)) is provided by the counter-propagating pump (G_(B)). Thefour-wave mixing product has been computed according to:

$X_{F}^{\prime} = \frac{\left\langle \left( {i_{1} - \left\langle i_{1} \right\rangle} \right)^{2} \right\rangle}{\left\langle i_{1} \right\rangle^{2}}$where i₁ is the photodiode current corresponding to a received “1”value.

In this example, it is assumed that 0.5 dB of gain saturation, i.e.,saturation effects that cause a 0.5 dB loss of gain represents a maximumtolerable level of saturation for the Raman amplifier of each span.Above this limit, cross-gain modulation causes intolerable transmissionimpairments in the example of FIG. 2. A dotted line represents a contourof gain/power combinations causing 0.5 dB of saturation. It is alsoassumed that adequate WDM receiver performance requires that the linkachieve an 11 dB output optical signal to noise ratio (OSNR) as measuredover a 0.5 nm bandwidth, taking into account noise introduced by all theamplifiers (both the 25 Raman amplifiers and the 26 EDFAs). The solidline is a contour representing combinations of forward gain and inputpower per channel that give rise to this desired OSNR at the output ofRaman amplifier 113. The input power per channel is set by the EDFApreceding the Raman amplifier.

It will then be appreciated that the combination of forward Raman gainand channel power to be employed should be on the solid curve to achievethe desired OSNR while maximizing suppression of four-wave mixingproducts. To maintain less than 0.5 dB of saturation, the selectedgain/power combination should also be to the left of the dotted linecurve. One example of a gain/power combination 202 that meets thesecriteria is a forward gain of approximately 5.50 dB in combination witha per-channel input power of approximately −5 dBm. It will be seen thatthis corresponds to a four-wave mixing cross talk of approximately −31dB. By contrast, if only the counter-propagating pump 116 were used(G_(F)=0), achieving the same gain and signal to noise ratio would meana four-wave mixing product suppression level of only −24 dB,insufficient for correct WDM receiver operation. If only thecounter-propagating pump (i.e. G_(F)=0) were used and the input channelpower were set to achieve −31 dB of four-wave mixing crosstalk, an OSNRof approximately only 7.5 dB would be obtained. It has been found thatforward gains of greater than 4 dB are often particularly advantageousin suppressing four-wave mixing products and achieving good OSNRperformance.

Once G_(F) has been selected, the backward gain G_(B) is selected bysubtracting G_(F) from the gain allocated to Raman amplifier 113, e.g.,15 dB in the depicted example. The power level of pump 114 is adjustedempirically to achieve the desired G_(F) value and the power level ofpump 116 is adjusted empirically to achieve the desired G_(B) value.

FIG. 3 is a graph depicting the relationship between cross-gainmodulation and gain saturation over all 25 spans according to oneembodiment of the present invention. The graph assumes a typicaldistribution of chromatic dispersion and chromatic dispersioncompensation through the link. This graph further assumes that the pumpsemit energy at 1445 nm. FIG. 3 is presented to support the selection of0.5 dB as a desired maximum saturation level. It is seen that cross-gainmodulation is suppressed by 30 dB for a gain saturation of 0.5 dB andpower per channel of −5 dBm. This is deemed to be sufficient suppressionfor typical WDM receiver operation.

Another important Raman amplifier impairment to control is doubleRayleigh backscattering. FIG. 4 is a graph depicting the relationshipbetween double Rayleigh back-scattering and Raman gain according to oneembodiment of the present invention. FIG. 4 assumes the use of TW-RSfiber, an effective area of 55 μm², a Rayleigh back-scatteringcoefficient of 5.25×10−8 m⁻¹, a pump wavelength of 1445 nm, a signalwavelength of 1545 nm.

FIG. 4 shows the Raman backscattering product caused by either theco-propagating pump or counter-propagating pump. This product iscomputed using the techniques disclosed in P. Hansen et al., IEEEPhoton. Tech. Lett., Vol. 10, No1 (1998), p. 159, the contents of whichare herein incorporated by reference. To evaluate the backscatteringproduct suppression for a given configuration of Raman amplifier 113,one separately determines the suppression levels for the forward andbackward gains using the values given by FIG. 4 for the number of spansin the link. Then, the double Rayleigh back scattering noise levelscontributed by the forward and backward gain are computed given thesuppression levels and the signal level at the output level of Ramanamplifier 113. These noise levels are added and compared to the signallevel to obtain the double Rayleigh backscattering suppression level. Ingeneral, double Rayleigh backscattering suppression of greater than 30dB is typically required. For our previous example system whereG_(F)=5.5 dB and G_(B)=9.5 dB, the double Rayleigh backsckatteringsuppression is approximately 37.5 dB.

It will be appreciated that there are many combinations of forward gainand backward gain that will give rise to a system with adequate signalto noise ratio, four-wave mixing product suppression, double Rayleighbackscattering product suppression, cross-gain modulation productsuppression, etc. The graphical methods described above are only onepossible method of selecting forward and backward gain for Ramanamplifier 113 according to the invention. Alternatively, one couldselect a combination of forward gain and backward gain based on adesired double backscattering product suppression level, four wavemixing product suppression level, and signal to noise ratio and thenverify the gain saturation performance that would result from theselected gains. By employing both co-propagating and counter-propagatingpump energy, Raman amplifier 113 achieves combinations of output signalto noise ratio and four-wave mixing product suppression that cannot beachieved using only counter-propagating optical energy.

It is understood that the examples and embodiments that are describedherein are for illustrative purposes only and that various modificationsand changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication and scope of the appended claims and their full scope ofequivalents. For example, other optical components may be includedbetween components shown as being directly connected in FIG. 1.

1. In an optical communication system, apparatus for amplifying anoptical signal, said apparatus comprising: a fiber; and an optical pumpenergy source disposed to inject optical pump energy into said fiber ina co-propagating direction relative to a transmission direction of anoptical signal in said fiber to cause Raman amplification of said signalin accordance with a gain level greater than 4 dB; wherein either 1) fora selected signal to noise ratio, there is a greater four-wave mixingproduct suppression level than would be achieved using only acounter-propagating optical pump energy source to obtain said gain levelor 2) for a selected four-wave mixing product suppression level, thereis a higher signal to noise ratio than would be achieved using only saidcounter-propagating energy source to obtain said gain level.
 2. In anoptical communication system, apparatus for amplifying an opticalsignal, said apparatus comprising: a first optical pump energy sourcedisposed to inject optical pump energy into a fiber in a co-propagatingdirection relative to a transmission direction of said optical signal tocause Raman amplification of said signal in accordance with a first gainlevel; a second optical pump energy source disposed to inject opticalpump energy into said fiber in a counter-propagating direction relativeto said transmission direction of said optical signal to cause Ramanamplification of said signal in accordance with a second gain level,said optical signal experiencing a total gain level including said firstgain level greater than 4 dB and said second gain level; and whereineither 1) for a selected signal to noise ratio, there is a greaterfour-wave mixing product suppression level than would be achieved usingonly said second optical pump energy source to obtain said total gainlevel or 2) for a selected four-wave mixing product suppression level,there is a higher signal to noise ratio than would be achieved usingonly said second optical pump energy source to obtain said total gainlevel.
 3. The apparatus of claim 2 wherein said second gain level is setresponsive to said first gain level and said total gain level.
 4. Theapparatus of claim 2 wherein said first gain level and said second gainlevel are set responsive to a desired maximum double Rayleigh scatteringlevel.
 5. The apparatus of claim 2 wherein a power level of said firstoptical pump energy source is set responsive to said first gain level.6. The apparatus of claim 2 wherein a power level of said second opticalpump energy source is set responsive to said second gain level.
 7. Theapparatus of claim 2 further comprising said fiber.
 8. The apparatus ofclaim 2 further comprising: an Erbium-doped fiber amplifier in cascadewith said fiber.
 9. In an optical communication system, apparatus foramplifying an optical signal, said apparatus comprising: a first opticalpump energy source disposed to inject optical pump energy into a fiberin a co-propagating direction relative to a transmission direction ofsaid optical signal to cause Raman amplification of said signal inaccordance with a first gain level greater than 4 dB; and a secondoptical pump energy source disposed to inject optical pump energy intosaid fiber in a counter-propagating direction relative to saidtransmission direction of said optical signal to cause Ramanamplification of said signal in accordance with a second gain level;wherein either for a selected gain saturation level, said first opticalpump energy source has a power level set to achieve one of a desiredgain saturation level or a desired Rayleigh backscattering level, andsaid second optical pump energy source has a power level set to obtain adesired gain level given said power level set for said first opticalpump energy source; and wherein either 1) for a selected signal to noiseratio, there is a greater four-wave mixing product suppression levelthan would be achieved using only said second optical pump energy sourceto obtain said total gain level or 2) for a selected four-wave mixingproduct suppression level, there is a higher signal to noise ratio thanwould be achieved using only said second optical pump energy source toobtain said total gain level.
 10. The apparatus of claim 9 furthercomprising said fiber.
 11. The apparatus of claim 10 further comprisingan Erbium-doped fiber amplifier in cascade with said fiber.
 12. In anoptical communication system, a method for amplifying an optical signalwithin a fiber by exploiting Raman effects to achieve a desired gainlevel, said method comprising: injecting co-propagating optical pumpenergy into said fiber to cause Raman amplification according to a firstgain level greater than 4 dB; injecting counter-propagating optical pumpenergy into said fiber to cause Raman amplification according to asecond gain level; and wherein either 1) for a selected signal to noiseratio at an output of said fiber, there is a greater four-wave mixingproduct suppression level than would be achieved injecting only saidcounter-propagating optical pump energy to obtain said desired gainlevel or 2) for a selected four-wave mixing product level, there is ahigher signal to noise ratio than would be achieved using injecting onlysaid counter-propagating optical energy to obtain said desired gainlevel.
 13. The method of claim 12 further comprising: further amplifyingsaid signal within an Erbium-doped fiber amplifier.
 14. In an opticalcommunication system, apparatus for amplifying an optical signal withina fiber by exploiting Raman effects to achieve a desired gain level,said apparatus comprising: means for injecting co-propagating opticalpump energy into said fiber to cause Raman amplification according to afirst gain level greater than 4 dB; means for injectingcounter-propagating optical pump energy into said fiber to cause Ramanamplification according to a second gain level; and wherein either 1)for a selected signal to noise ratio at an output of said fiber, thereis a greater four-wave mixing product suppression level than would beachieved injecting only said counter-propagating optical pump energy toobtain said desired gain level or 2) for a selected four-wave mixingproduct level, there is a higher signal to noise ratio than would beachieved injecting only counter-propagating optical energy to obtainsaid desired gain level.
 15. The apparatus of claim 14 furthercomprising: means for further amplifying said signal within anErbium-doped fiber amplifier.